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A line makes an angel theta with each o...

A line makes an angel `theta` with each of the x-and z-axes. If the angel `beta,` which it makes with the y-axis, is such that `sin^2beta=3sin^2theta`,then `cos^2theta` equals a. `2/3` b. `1/5` c. `3/5` d. `2/5`

A

`(2)/(3)`

B

`(1)/(5)`

C

`(3)/(5)`

D

`(2)/(5)`

Text Solution

Verified by Experts

Here `sin^(2)beta=3sintheta" "(i)`
By the question, `cos^(2)theta+cos^(2)theta+cos^(2)beta=1" "(ii)`
`impliescos^(2)beta=1-2cos^(2)theta" "(iii)`
Adding (i) and (iii), we get
`1=1+3sin^(2)theta-2costheta`
`=1+3(1-cos^(2)theta)-2cos^(2)theta`
or `5cos^(2)theta=3`
or `cos^(2)theta=(3)/(5)`
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Knowledge Check

  • A line makes the same angle theta with each of the X and Z-axes. If the angle beta , which it makes with Y-axis, is such that sin^(2)beta=3sin^(2)theta , then cos^(2)theta equals

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